B₂[∞]-sequences of square numbers
Beatty sequences and multiplicative number theory
Bemerkung zu einer Anwendung des Bertrandschen Postulats in der Zahlentheorie.
Binomials transformation formulae for scaled Fibonacci numbers
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Bohr local properties of
Bounds for the 3x+1 problem using difference inequalities
Bounds for the Kolakoski sequence.
Bounds on ternary cyclotomic coefficients
Büchi Sequences in Local Fields and Local Rings
We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring of p-adic integers. In there are only finite but arbitrarily long Büchi sequences.
Buck's measure density and sets of positive integers containing arithmetic progression
Carmichael numbers composed of primes from a Beatty sequence
Let α,β ∈ ℝ be fixed with α > 1, and suppose that α is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence . We conjecture that the same result holds true when α is an irrational number of infinite type.
Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.
Chebyshev polynomials and the modulary group of level p
Closed-form expression for Hankel determinants of the Narayana polynomials
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana...
Coefficients of a relative of cyclotomic polynomials
Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences.
Complementary equations and Wythoff sequences.
Complete sequences of sets of integer powers
Complexity of Hartman sequences
Let be an ergodic translation on the compact group and a continuity set, i.e. a subset with topological boundary of Haar measure 0. An infinite binary sequence defined by if and otherwise, is called a Hartman sequence. This paper studies the growth rate of , where denotes the number of binary words of length occurring in . The growth rate is always subexponential and this result is optimal. If is an ergodic translation
Computing tournament sequence numbers efficiently with matrix techniques.